 | Arthur Schultze - 1901 - 260 pages
...equal respectively to the hypotenuse and an acute angle of the other. PROPOSITION XIII. THEOREM 100. An exterior angle of a triangle is equal to the sum of the two remote interior angles. f / B CD Hyp. Z ACD is an exterior angle of A ABG. To prove Z ACD =... | |
 | Thomas Smith (D.D.) - Euclid's Elements - 1902 - 244 pages
...a straight line parallel to a given straight line. And so he was able in Prop. 32 to prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. Thus it appears that Prop. 16 is only a scaffolding for the erection of Prop. 32.... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...triangle are known, the third can be formed by subtracting their sum from two right angles. Corollary VI. An exterior angle of a triangle is equal to the sum of the two opposite interior angles, as angle BCD = angle A + angle B. THEOREM XVII. 77. If two triangles... | |
 | United States Naval Academy - 1904 - 980 pages
....^^^«(tO.-u (b) Given л- + xy = 70 and xy — y* =12, find .т and y. GEOMETRY. I. (a) Prove that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Define axiom and postulate, and give an example of each. Define trapezoid,... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...COR. 7. In an equiangular triangle, each angle is one third of two right angles, or 60°. 137. COR. 8. An exterior angle of a triangle is equal to the sum of the two opposite interior angles, and therefore greater than either of them. PROPOSITION XIX. THEOREM.... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...its equal, ZA.and for /.BCE its equal, ZB, Ax. 8. ZA + /.B + /.BCA = 2 rt. A. 0. E. J>. 135. COR. 1. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. 136. COR. 2. The sum of any two angles of a triangle is less than... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...LECD its equal, Z.4,and for LBCE its equal, LB, Ax. 8, /A+ ZB + Z BGA - 2 rt. Z . 0- EB 135o Con. 1. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. 136o COR. 2. The sum of any two angles of a triangle is less than... | |
 | George Clinton Shutts - 1905 - 260 pages
...perimeter of a triangle is less than twice the sum of the medians. PROPOSITION XXVIII. 119, Theorem. An exterior angle of a triangle is equal to the sum of the opposite interior angles. Let ABC represent a triangle, D AC an erterior angle, and B and C the... | |
 | Francis Fisher Browne - American literature - 1906 - 894 pages
...diagram on the floor of his play-room, the thirty-second proposition of the first book of Euclid (the exterior angle of a triangle is equal to the sum of the two interior and opposite angles, and the three angles of a triangle together equal two right angles). In secret,... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...therefore, the third angle is equal to 180° - (44° 21' 30" + 110° 53' 45") = 24° 44' 45". Ans. (4) An exterior angle of a triangle is equal to the sum of the opposite-interior angles (Art. 68) . The sum of the opposite-interior angles is, therefore, 104°... | |
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 
